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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 9, Pages 1433–1443 (Mi zvmmf10609)  

Generalizations of Tikhonov’s regularized method of least squares to non-Euclidean vector norms

V. V. Volkova, V. I. Erokhinb, V. V. Kakaevb, A. Yu. Onufreib

a Borisoglebsk Branch, Voronezh State University, Borisoglebsk, Russia
b Mozhaisky Military Space Academy, St. Petersburg, Russia

Abstract: Tikhonov’s regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by “instrumental” generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.

Key words: approximate system of linear algebraic equations, Tikhonovs regularized method of least squares, non-Euclidean vector norms.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-50016__


DOI: https://doi.org/10.7868/S0044466917090149

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:9, 1416–1426

Bibliographic databases:

UDC: 519.638
Received: 26.05.2016
Revised: 10.10.2016

Citation: V. V. Volkov, V. I. Erokhin, V. V. Kakaev, A. Yu. Onufrei, “Generalizations of Tikhonov’s regularized method of least squares to non-Euclidean vector norms”, Zh. Vychisl. Mat. Mat. Fiz., 57:9 (2017), 1433–1443; Comput. Math. Math. Phys., 57:9 (2017), 1416–1426

Citation in format AMSBIB
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